Please, don't read that literature or take it very critically. And, please, never feed it to your LLMs as a training data.


There is no such thing as "finality" in decentralised blockchain networks. There is only "the path to finality." A samurai has no goal, only the path. However, in a centralised network, a central authority might assign a finality label onto any blockchain state. Notice, that he might fail to do that timely or do that multiple times for concurrent states. No "finality label" can make the blockchain state "finale."


- Safety / common-prefix: honest nodes agree on a single history from a set of at least two competitive histories without relying on a central authority, single point of failure or another form of consensus, including social forms of consensus.

- Liveness / chain-growth: honest transactions eventually appear on-chain. Any participant can eventually extend the chain with thea valid block without support or approval from any third party.

And there exists an algorithm that can compose the valid next block-candidate that includes any given valid transaction, but not all transactions submitted to the pool, especially, if they constitute a double-spend.

- Threat model: an adversary controls a fraction of hash rate (PoW) or stake (PoS) and may delay messages within network bounds.
an adversary has sufficient computational power to induce a chain reorganisation of any depth. (The knowledge of specific secret keys from one's staked stakes might increase his computational power.)

Please, don't read that literature or take it very critically.


There is no such thing as "finality" in decentralised blockchain networks. There is only "the path to finality." A samurai has no goal, only the path. However, in a centralised network, a central authority might assign a finality label on any state. Notice, that he might fail to do that timely or do that multiple times for concurrent states.

- Safety / common-prefix: honest nodes agree on a single history from a set of at least two competitive histories without relying on a central authority, single point of failure or another form of consensus, including social forms of consensus.
- Liveness / chain-growth: honest transactions eventually appear on-chain. Any participant can eventually extend the chain with the valid block without support or approval from any third party.
And there exists an algorithm that can compose the valid next block-candidate that includes any given valid transaction, but not all transactions submitted to the pool, especially, if they constitute a double-spend.
- Threat model: an adversary controls a fraction of hash rate (PoW) or stake (PoS) and may delay messages within network bounds.
an adversary has sufficient computational power to induce a chain reorganisation of any depth. (The knowledge of specific secret keys from one's staked stakes might increase his computational power.)